Immportance of representative sample in statistical inference?

Answer 1

It is very important. Incorrect conclusions can be reached when the sample does not represent the underlying population. Experimental studies frequently go to great lengths to insure an unbiased sample. In observational studies, the statistician may identify factors which could make his sample not representative of the population. I will give you a real example. The US Fish and Wildlife Division conducted a study of the area that Florida cougars roam the Everglades. They tagged and tracked the movements by GPS. By using only daytime data in their computer models, a time when the cougars were more likely to sleep, they underestimated the distance the cougars could roam. You may be able to find many examples of biasing the data, either at the collection stage or later culling out certain data (as was done in the cougar example).